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Find the average rate of change of $f(x) = -x + 6$ between $x = 4$ and $x = 4 + h$ , where $h \neq 0$ . $\newline$ Simplify your answer. Your answer may be a number or an expression in terms of $h$ .

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Average rate of change I

Full solution

Q. Find the average rate of change of

f(x) = -x + 6

between

x = 4

and

x = 4 + h

, where

h \neq 0

.

\newline

Simplify your answer. Your answer may be a number or an expression in terms of

h

.

Calculate $f(4)$ : Calculate $f(4)$ and $f(4 + h)$ to use in the average rate of change formula. $\newline$ $f(4) = -(4) + 6 = 2$ $\newline$ $f(4 + h) = -(4 + h) + 6 = 2 - h$
Use average rate of change formula: Use the average rate of change formula: $(f(a+h) - f(a)) / h$ . $\newline$ Substitute $f(4)$ and $f(4 + h)$ into the formula: $\newline$ $(2 - h - 2) / h = -h / h$
Simplify expression: Simplify the expression $-\frac{h}{h}$ . $-\frac{h}{h} = -1$

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